Rogue waves and analogies in optics and oceanography

Over a decade ago, an analogy was drawn between the generation of large ocean waves and the propagation of light fields in optical fibres. This analogy drove numerous experimental studies in both systems, which we review here. In optics, we focus on results arising from the use of real-time measurement techniques, whereas in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. This Review of the work in hydrodynamics includes results that support both nonlinear and linear interpretations of rogue wave formation in the ocean, and in optics, we also provide an overview of the emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems. We discuss the insights gained from the analogy between the two systems and its limitations in modelling real-world ocean wave scenarios that include physical effects that go beyond a one-dimensional propagation model. An analogy between wave propagation in hydrodynamics and in optics has yielded new insights into the mechanisms leading to the formation of giant rogue waves on the ocean. We review experimental progress and field measurements in this area.